One Click Prep | Sujoy Kumar Datta

Let us take a question on mixtures. We will try to solve it using five different methods A 80 liter solution contains 20% alcohol by volume. A part of the solution is removed and replaced with pure alcohol to bring the alcohol concentration to 25%. What is the volume of the solution that was removed? Method 1 - Using basic percentage computations and setting up an equation Volume of alcohol in the 80 liters solution = 20% of 80 = 20 × 80 ÷ 100 = 16 liters Let volume of solution removed = v liters This will also have 20% alcohol ⇒ Volume of alcohol removed = 20 × v ÷ 100 = 0.2v liters Volume of alcohol added = v liters (Note: replace imples adding a quantity equal to what was removed) Thus, total alcohol volume = (16 - 0.2v + v) = (16 + 0.8v) liters Total solution volume = 80 liters Thus, required percent = [(16 + 0.8v) ÷ 80] × 100 Thus, we have: [(16 + 0.8v) ÷ 80] × 100 = 25 ⇒ 16 + 0.8v = 20 ⇒ v = 5 liters - Answer Method 2 - Using the fact that the concentration of alcohol remains u...

How to solve Removal and replacement questions We often get questions involving  removal and replacement of mixtures where a part of a mixture is removed and replaced by some other solution. Say, a vessel contains different constituents in some given ratio. A fraction of the solution is removed and some quantity of some constituent is added to the solution. This process is repeated multiple times and the final ratio of constituents in the mixture has to be determined. Though this looks very complicated, we can solve it simply, in fact, in a single line! We just need to understand the fact that if a fraction,  f  of the solution is removed, the same fraction of each constituent also gets removed, and hence, the fraction  (1-f)  of each constituent is left, and as a result, after removal, the ratio of the constituents remains unchanged. This is very easy to understand. Say, you have a sugar solution in a glass and you drink a part of it. The remaining part would t...

Percentage & Percentage change Percent (read as per cent) means ‘every hundred’, or, essentially, ‘out of 100’. If we are given a fraction, we can simply convert it to a percentage by multiplying 100. Say, we have ½, which, when multiplied with 100 becomes ½ x 100 = 50%. What do we mean by a percentage change? Say, a person has 20 chocolates. If his number of chocolates is increased by 10%, what does it mean? First of all, let us see what is doesn’t mean: after the increase, the number of chocolates with him is  NOT  20 + 10 = 30, nor is it 20 +  10 / 100  = 20.1 When we talk of a percent increase, we must understand on what  BASE VALUE  is the percentage change working on. In this case, obviously, the 10% increase is 10% of the number of chocolates he has, i.e. 20. Thus, the number of chocolates with him would become: 20 + 10% of 20 = 20 + 20 x  10 / 100  = 22 Observe that:  20 + 20 x  10 / 100  = 20 x (1 +  10 / 100 ) = 2...

How important is the GMAT? Well, many schools nowadays are test-optional. If that were the case, why do you even need to prepare for and write the test? Couldn’t the time and effort and cost spent in preparing for the test be spent more effectively elsewhere? Let us look at some of the advantages that a (high) GMAT score brings along. GMAT is one of the toughest exams worldwide. Getting prepared for it needs a lot of self-discipline. Getting a top score in such a test shows that you are focussed and serious about your application A high GMAT score => Better chances into getting admission to a higher ranked school. Your GMAT score has approximately 22% weightage in your application (with your Quant score having additional weightage). No doubt the GMAT score is a vital part of your application A good GMAT score helps you to stand out from an over-represented candidate pool (for example, IT guys from India) The GMAT tests your reasoning and quantitative skills. Both of these are very i...